Search: id:A039622
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%I A039622
%S A039622 1,1,2,42,24024,701149020,1671643033734960,475073684264389879228560,
%T A039622 22081374992701950398847674830857600,
%U A039622 220381378415074546123953914908618547085974856000
%N A039622 Number of n X n Young tableaux.
%C A039622 Number of arrangements of 1,2,..,n*n in an n*n matrix such that each 
               row and each column is increasing.
%C A039622 Factor g_n in formula for 2n-th moment of Riemann zeta function on the 
               critical line. (See Conrey article.) - Michael Somos, Apr 15 2003
%C A039622 Number of linear extensions of the n X n lattice. - Mitch Harris (Harris.Mitchell 
               (AT) mgh.harvard.edu), Dec 27, 2005
%D A039622 The problem for a 5 X 5 array was recently posed and solved in the College 
               Mathematics Journal. The solution is in Vol. 30 (1999), no. 5, pp. 
               410-411.
%D A039622 J. B. Conrey, The Riemann Hypothesis, Notices Amer. Math. Soc., 50 (No. 
               3, March 2003), 341-353. See p. 349.
%D A039622 J. S. Frame, G. de B. Robinson and R. M. Thrall, The hook graphs of a 
               symmetric group, Canad. J. Math. 6 (1954), pp. 316-324.
%D A039622 M. du Sautoy, The Music of the Primes, Fourth Estate / HarperCollins, 
               2003; see p. 284.
%H A039622 J. B. Conrey, <a href="http://www.ams.org/notices/200303/fea-conrey-web.pdf">
               The Riemann Hypothesis</a>
%H A039622 <a href="Sindx_Y.html#Young">Index entries for sequences related to Young 
               tableaux.</a>
%F A039622 a(n) = (n^2)! / (product k=1, ..., 2n-1 k^(n - |n-k|))
%F A039622 a(n) = 0!*1!*..*(k-1)! *(k*n)! / ( n!*(n+1)!*..*(n+k-1)! ) for k=n.
%F A039622 a(n) = A088020(n)/A107254(n) = A088020(n)*A000984(n)/A079478(n). - Henry 
               Bottomley (se16(AT)btinternet.com), May 14 2005
%F A039622 a(n) = A153452(prime(n)^n).- Naohiro Nomoto, Jan 01 2009
%e A039622 Using the hook length formula, a(4) = (16)!/(7*6^2*5^3*4^4*3^3*2^2) = 
               24024.
%o A039622 (PARI) a(n)=if(n<0,0,(n^2)!*prod(k=0,n-1,k!/(n+k)!))
%Y A039622 Main diagonal of A060854. a(2)=A000108(2), a(3)=A005789(3), a(4)=A005790(4), 
               a(5)=A005791(5).
%Y A039622 Sequence in context: A162678 A124103 A152286 this_sequence A130506 A052078 
               A069544
%Y A039622 Adjacent sequences: A039619 A039620 A039621 this_sequence A039623 A039624 
               A039625
%K A039622 nonn,nice,easy
%O A039622 0,3
%A A039622 Floor van Lamoen (fvlamoen(AT)hotmail.com)
%E A039622 References, correction and extension from Stephen G. Penrice (spenrice(AT)ets.org), 
               Jun 15 2000

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